1. Field of the Invention
The present invention generally relates to a phase-demodulation method for demodulating a phase-modulated communication signal. More particularly, the present invention relates to a phase-demodulation method for minimizing the phase error generated by noise.
2. Description of the Related Art
Typically, a phase-modulation/demodulation method in a communication field simultaneously varies and transmits the phase of sinusoidal waves of a predetermined frequency at intervals of a predetermined phase. Several problems causing distortions of the sinusoidal waves are created in such a process. An example of this is when a communication signal is loaded on a carrier wave and interference with other signals occurs, or noise is undesirably added to a desired signal, etc., thereby distorting the sinusoidal waves. If a signal having the distorted sinusoidal waves is received at a reception end, a frequency of the signal is adjusted down to an initial frequency and filtered to be proper to a signal bandwidth in such a way that the signal is demodulated to an original signal. Commonly, in case of describing the physical characteristics of a modulation/demodulation process, the above steps are simplified as a procedure for adding an independent Gaussian noise to an original signal. Provided that the Gaussian noise is not considered, signal waves received at a reception end can be represented by the following Equation 1.                               w          ⁡                      (            φ            )                          =                              ∑            m                    ⁢                                    α              m                        ⁢                          ⅇ                              ⅈ                ⁢                                                                   ⁢                                  m                  ⁡                                      (                                          φ                      +                                              φ                        0                                                              )                                                                                                          [                  Eq          .                                           ⁢          1                ]            
In case of a digital phase demodulation, a demodulated signal is sampled at more than twice the original signal frequency. In this case, in case of representing a sampling interval as a phase interval of δ, a k-th sampled value is represented by the following Equation 2.                               w          k                =                              ∑            m                    ⁢                                    α              m                        ⁢                          ⅇ                              ⅈ                ⁢                                                                   ⁢                m                ⁢                                                                   ⁢                                  φ                  0                                                      ⁢                          ⅇ                              ⅈ                ⁢                                                                   ⁢                mk                ⁢                                                                   ⁢                δ                                                                        [                  Eq          .                                           ⁢          2                ]            
A method for demodulating values called I and Q signals from the above sampling signals is called a phase-demodulation algorithm. Such phase-demodulation algorithm can be represented by the following Equation 3.                                                         S              =                            ⁢                                                ∑                                      k                    =                    0                                                        K                    -                    1                                                  ⁢                                                      c                    k                                    ⁢                                      w                    k                                                                                                                                          c                k                            ≡                            ⁢                                                a                  K                                +                                  ⅈ                  ⁢                                                                           ⁢                                      b                    k                                                                                                                                          ∴                S                            =                            ⁢                                                ∑                                      k                    =                    0                                                        K                    -                    1                                                  ⁢                                                      (                                                                  a                        k                                            +                                              ⅈ                        ⁢                                                                                                   ⁢                                                  b                          k                                                                                      )                                    ⁢                                      w                    k                                                                                                                          I              =                            ⁢                              real                ⁢                                  {                  S                  }                                                                                                        Q              =                            ⁢                              imag                ⁢                                  {                  S                  }                                                                                        [                  Eq          .                                           ⁢          3                ]            
Characteristics of the phase-demodulation algorithm are determined by a coefficient Ck used in a complex phasor S.
FIG. 1A is a view illustrating a constellation in a conventional 3-sample algorithm (i.e., 3-point algorithm). FIG. 1B is a view illustrating a phase-error distribution in a conventional 3-sample algorithm. FIG. 2A is a view illustrating a constellation in a conventional 4-sample algorithm (i.e., 4-point algorithm). FIG. 2B is a view illustrating a phase-error distribution in a conventional 4-sample algorithm.
Referring to FIGS. 1A and 2A, in case of considering an axis of 0° and an axis of 90° as reference lines, FIG. 1A using the 3-point algorithm shows that symbols α and β each have errors of almost 90° and the distribution of the errors is in a wide range. FIG. 2A using the 4-point algorithm shows that values of the symbols γ and δ are much less than the symbols α and β.
In addition, as shown in FIGS. 1B and 2B, the 4-point algorithm reduces the error distribution much more than the 3-point algorithm does.
It is noted that the aforesaid digital phase-demodulation algorithms more accurately calculate a signal phase in proportion to the number of sampling times and is also resistant to noise.
However, it is impossible to increase the number of sampling times indefinitely in case of a symbol rate of a very high value. Also, a processor used for phase calculation may receive an excessive load during a phase calculation time.
Therefore, there is a need for an optimized algorithm for calculating an accurate phase using a minimum number of sampling times and a minimum number of calculation times.